B: Nano-Electronics

At the nano-scale, the inherent quantum nature of electrons as well as interaction effects gain increasing importance. The understanding and control of the associated phenomena, which show up in a variety of physical systems of reduced dimensionality, is the focus of research area B. Well studied systems are quantum dots and point contacts in two-dimensional electron gases as well as atomic-scale point contacts, clusters, and molecules with tailored properties incorporated in appropriate circuits. Much attention has been devoted to carbon nanotubes and graphene nanoribbons. Metallic, superconducting, and magnetic nanostructures as well as heterostructures made of these materials show a different, but similarly rich variety of quantum effects. Recently, topological insulators have been recognized as a new state of matter with fascinating properties. In what follows, we touch on a few of the relevant fields.

Nanoelectronic Devices

While already operating in the 10-nanometer regime, most present-day technologies for electronic devices and foreseeable extrapolations still rely on classical electron-transport concepts. On the other hand, at these scales the understanding and taming of non-classical effects becomes increasingly important, and a growing number of ideas are being developed how to control and even to make use of them. Indeed, quantum devices already exist for specific applications: Single-electron transistors are used as ultra-sensitive voltage probes and current standards; quantum point contacts allow counting the passage of individual electrons; superconducting quantum circuits are used to prepare specific photon states and to probe the sources and microscopic properties of noise; molecule-based circuits can be used as sensors for residual gases. In view of such examples, the expectations are high for further manifestations of quantum transport, as well as applications in the areas of nano-electronics, spin­tronics, sensor technologies, and metrology.

Graphene and Topological Phases

Research devoted to the properties of graphene has grown dramatically after 2004, when A. Geim and K. Novoselov reported their studies of mono-atomic graphite layers. Various ways of tuning parameters, such as the carrier density, have been developed, and various novel quantum transport properties were discovered. The exceptional properties of graphene make this material highly interesting from the point of view of both fundamental physics and potential applications in the field of carbon-based nano-electronics. More recently, the concept of topologically protected metals and insulators in low-dimensional structures has attracted the attention of theoretical and experimental groups. The term “topological insulator” refers to a bulk band insulator with gapless surface states protected for topological reasons. Heterostructures involving topological insulators and graphene or superconductors promise to display novel quantum transport properties.

Solid State Quantum-State Engineering

Quantum-state engineering, i.e., the control of the coherent dynamics of quantum-mechanical systems, opens fascinating perspectives for information processing and novel measurement principles. Solid-state quantum bits appear most promising because they can be embedded in electronic circuits. In particular, the Josephson junction technology has reached a stage where all relevant operations have been demonstrated, multi-qubit circuits have been fabricated, and simple quantum algorithms have been implemented. More­over, a new field of “circuit quantum electrodynamics” has emerged where Josephson qubits are coupled to microwave resonators. Many effects known from quantum optics have been observed with unprecedented quality, incl. the high-fidelity creation of specific Fock states and the operation of single-qubit lasers.

Computational Methods

While for non-interacting systems the Landauer approach provides a versatile theoretical tool, there is currently no general approach to finite-bias transport through correlated systems, in spite of many efforts. Formally, the problem is solved by the Meir-Wingreen formula using Keldysh Green’s functions. However, the evaluation of these formulas for interacting systems is generally based on approximations, like the perturbative Keldysh or functional renormalization group (RG) approach. In the time-dependent numerical RG one applies the Wilson RG method to extract the Keldysh Green’s functions of the steady state. In Quantum Monte Carlo (QMC) approaches one either works in imaginary time or one evaluates the determinants resulting from the path-integral formulation. Another strategy, based on the direct propagation of wave packets, is used within time-dependent density functional theory (DFT) and density matrix (DM) RG. Out of these techniques the Keldysh, the QMC, and the time-dependent DMRG approaches also give access to correlation functions like shot noise.

Specific Goals

Our aim for the future in research area B is to explore and understand electronic properties of nanostructures induced by quantum-mechanical and interaction effects, with the vision to lay the basis for future nano-electronic circuitry. Our specific goals for the future are: (1) Develop new experimental and theoretical techniques to describe and probe correlation effects in various materials at low temperatures. (2) Investigate novel collective electron properties in superconductor-ferromagnet hybrids and topological insulators. (3) Explore the functionality of quantum coherent superconducting circuits and spin systems. (4) Study the non-conventional transport properties of carbon nanostructures. (5) Search for novel functionalities of nanostructured devices with potential for metrological and detector applications.

In the CFN reporting period 2006-2010, research area B comprised three projects: